p. 709
–716
(8)
Gait analysis plays an important role in healthcare and other applications. In the situation of ambulatory thigh movement estimation using accelerometers, the major challenges are non-linearity and uncertainty of thigh motion and variations of accelerometer measurement noise. In this study, the authors propose to use multiple motion models and noise models to meet these challenges. In order to adaptively select motion models and noise models to suit the thigh motion modes, feature vectors are derived from the acceleration signal in the wavelet domain for gait phases/modes detection. Based on the detection results, the right motion models and noise models are chosen, and an unscented Kalman filter is invoked to estimate the thigh movement using the chosen models. The experimental results have shown that the proposed method can estimate thigh movement accurately.

p. 717
–727
(11)
Multichannel sampling for bandlimited signals is fundamental in the theory of multichannel parallel analogue-to-digital (A/D) environment and multiplexing wireless communication environment. The analysis and application of multichannel sampling in the traditional Fourier domain have been extensively studied, but so far none of the research papers covering the reconstruction of multichannel sampling in the linear canonical transform (LCT) domain have been published. This study is to explore the multichannel sampling and reconstruction of bandlimited signals in the LCT domain. First, the multichannel sampling theorem for bandlimited signals with LCT is proposed, which is the generalisation of classical generalised Papoulis sampling expansion. Considering the signal reconstruction purpose, the authors present two schemes for the multichannel sampling with LCT. The first scheme is based on the conventional Fourier series and inverse LCT, whereas the other uses the generalised convolution systems. Second, by designing different LCT filters, the authors obtain the reconstruction method for the uniform sampling theorem, sampling from the signal and its derivative by using the derived multichannel sampling theorem and properties of the LCT. Last, the simulations are carried out to verify the correctness of the results. Moreover, the potential applications of the multichannel sampling are also presented.

p. 728
–738
(11)
It is well known that the partial sums of a Fourier series of a non-periodic analytic function on a finite interval exhibit spurious oscillations near the interval boundaries. This phenomenon is known as the Gibbs effect. The authors show that a similar phenomenon is observed for the fractional Fourier series (FrFS) of a function with jump discontinuities. The convergence of FrFS is discussed and proved in a theorem. Specifically, the present work proves the uniform convergence of the FrFS for a non-periodic analytic function in the smooth region. The maximum amplitude of the oscillations for the FrFS remains constant (the Gibbs constant), similar to that for a classical Fourier series expansion. Finally, three numerical examples are investigated to demonstrate that the Gibbs constant for an FrFS is the same as for a Fourier series.

p. 739
–747
(9)
The authors consider underwater acoustic (UWA) channel estimation based on sparse recovery using the recently developed homotopy algorithm. The UWA communication system under consideration employs orthogonal frequency-division multiplexing (OFDM) and receiver preprocessing to compensate for the Doppler effect before channel estimation. The authors first extend the original homotopy algorithm which is for real-valued signals to the complex field. The authors then propose two enhancements to the sparse recovery-based UWA channel estimator by exploiting the UWA channel temporal correlations, including the use of a first-order Gauss–Markov model and the recursive least-squares algorithm for channel tracking. Moreover the authors propose a scheme to optimise the pilot placement over the OFDM subcarriers based on the discrete stochastic approximation. Simulation results show that the homotopy algorithm offers faster and more accurate UWA channel estimation performance than other sparse recovery methods, and the proposed enhancements and pilot placement optimisation offer further performance improvement.

p. 748
–756
(9)
Chaotic signals show many advantages in the application of radar systems. The technique described in this study focuses on the chaotic behaviour of the chaotic-based frequency- and phase-modulated signals. Chaotic-based frequency- and phase-modulated signals are introduced and analysed. Theoretical analysis points out that the initial chaotic map's phase structure is destroyed by frequency or phase modulation, which may be the direct reason that induces uncertain chaotic behaviours of the modulated signals based on chaos. Furthermore, a sufficient condition for chaotic maps to ensure the chaotic-based frequency-modulated signals remaining chaotic is discussed, and an initial sensitive correlation function for the chaotic-based phase-modulated signals is defined to estimate the possibility of chaotic behaviours remaining. Both theoretical analysis and computer simulation present the uncertain property of chaotic behaviours for chaotic-based signals, which induces better or worse signal performances depending on different chaotic maps and different signal modulation. It is also demonstrated that chaotic behaviours of the modulated signals based on chaos do not certainly provide satisfying performances for radar applications.

p. 757
–766
(10)
This study proposes a class of H∞ filter design for linear time-delay system. The time delay considered here is assumed to be satisfying a certain stochastic characteristic. Corresponding to the probability of the delay taking value in different intervals, a stochastic variable satisfying Bernoulli random binary distribution is introduced and a new system model is established by employing the information of the probability distribution. Then new criteria is derived for the filtering-error systems, which can lead to much less conservative analysis results. It should be noted that the solvability of the obtained criteria depend not only on the size of the delay, but also the probability distribution of it. At last, numerical examples are given to demonstrate the effectiveness and the merit of the proposed method.

p. 767
–775
(9)
This study proposes a real-time joint angle estimation method of human elbow by processing a biomedical signal of surface synergistic EMG (electromyogram) measured between biceps brachii and triceps brachii simultaneously. Actually, the EMG is known as a non-stationary signal, but the authors assume that it is quasi-stationary because a physical or physiological system has limitations in the rate at which it can change its characteristics. Based on the assumption, a pre-processing method to obtain pre-angle values from the raw synergistic EMG signal is firstly suggested, and then a method to estimate the joint angle through normalisation when there are external loads is discussed. In addition, an optimisation method to minimise the error between the normalised angle and real joint angle is proposed. Finally, the authors show the effectiveness of the suggested algorithm through experimental results.